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Table 3 Initial guess of parameters and anticipated tolerance of approximation

From: A rational cubic trigonometric approximation scheme of the generalized Cornu spirals

Approximation schemes

Values of parameters/anticipated tolerance (\( \varepsilon \))

Circular arc

Cornu spiral

Logarithmic spiral

Non-inflecting GCS

Normalized GCS

G 2-approximation

\( d_{1} \)

0.5

1.515

5

1.1

2

d 3

0.5

1.426

1.7

1.1

2

\( \varepsilon \)

3.59 × 10−2

2.78 × 10−2

6.42 × 10−2

1.10 × 10−2

0.05

G 1-approximation

\( d_{1} \)

0.457

1.45

2.28

1.089

2

d 3

0.688

1.40

3.19

0.899

2

μ 1

0.876

0.67

0.88

1.55

0.8

μ 2

0.812

0.899

0.787

1.32

0.8

\( \varepsilon \)

3.59 × 10−2

2.78 × 10−2

6.42 × 10−2

1.10 × 10−2

0.05